Abstract:
Certain inventory items are living organisms, for example livestock, and are therefore capable of growing during the replenishment cycle. These items often serve as various saleable food items downstream in supply chains. The purpose of this paper is to
develop a lot sizing model for growing items if the supplier of the items ofers incremental quantity discounts. A mathematical
model is derived to determine the optimal inventory policy which minimises the total inventory cost in both the owned and
rented facilities. A solution procedure for solving the model is developed and illustrated through a numerical example. Sensitivity
analysis is performed to demonstrate the response of the order quantity and total costs to some key input parameters. Incremental quantity discounts result in reduced purchasing costs; however, ordering very large quantities has downsides as well. The
biggest downsides include the increased holding costs, the risks of running out of storage capacity and item deterioration since
the cycle time increases if larger quantities are purchased. Owing to the importance of growing items in the food supply chains,
the model presented in this article can be used by procurement and inventory mangers when making purchasing decisions.
